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Abstract: Systems whose organization displays causal asymmetry constraints, fromevolutionary trees to river basins or transport networks, can be oftendescribed in terms of directed paths causal flows on a discrete state space.Such a set of paths defines a feed-forward, acyclic network. A key problemassociated with these systems involves characterizing their intrinsic degree ofpath reversibility: given an end node in the graph, what is the uncertainty ofrecovering the process backwards until the origin? Here we propose a novelconcept, \textit{topological reversibility}, which rigorously weigths suchuncertainty in path dependency quantified as the minimum amount of informationrequired to successfully revert a causal path. Within the proposed framework wealso analytically characterize limit cases for both topologically reversibleand maximally entropic structures. The relevance of these measures within thecontext of evolutionary dynamics is highlighted.



Author: Bernat Corominas-Murtra, Carlos Rodríguez-Caso, Joaquín Goñi, Ricard Solé

Source: https://arxiv.org/



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